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Polynomial Division Calculator

Divide a polynomial by (x - r) using synthetic division.

Introduction

Polynomial Division Calculator — Divide a polynomial by (x - r) using synthetic division. Enter Coefficients (highest degree first, comma separated), Divisor root (x - r) to get an instant, accurate result.

Formula

Performs synthetic division of a polynomial (coefficients highest-degree first) by (x − r), producing a quotient polynomial one degree lower plus a remainder.

Step-by-step

  1. Enter the Coefficients (highest degree first, comma separated).
  2. Enter the Divisor root (x - r).
  3. Click Calculate to see your result instantly.

Real-world example

Example: With Coefficients (highest degree first, comma separated) = 1, -3, 2, Divisor root (x - r) = 1, the Polynomial Division Calculator gives Quotient: 1, -2, Remainder: 0.

Frequently Asked Questions

What does the remainder tell you?
If the remainder is 0, (x − r) divides the polynomial evenly, meaning r is a root of the polynomial.
Does this work for any divisor?
Synthetic division here specifically divides by a linear factor (x − r), not an arbitrary polynomial divisor.
What inputs does the Polynomial Division Calculator need?
You'll need to provide: Coefficients (highest degree first, comma separated), Divisor root (x - r). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Polynomial Division Calculator?
The Polynomial Division Calculator applies the formula exactly as calculated — Performs synthetic division of a polynomial (coefficients highest-degree first) by (x − r), producing a quotient polynomial one degree lower plus a remainder. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Polynomial Division Calculator free to use?
Yes, the Polynomial Division Calculator is completely free, requires no signup, and runs instantly in your browser.

About the Polynomial Division Calculator

The Polynomial Division Calculator uses a real, verifiable formula — Performs synthetic division of a polynomial (coefficients highest-degree first) by (x − r), producing a quotient polynomial one degree lower plus a remainder. — so results are accurate every time, not an approximation.